Tracking attracting manifolds in flows

Abstract

This paper presents a collaborative control strategy designed to enable a team of robots to track attracting Lagrangian coherent structures (LCS) and unstable manifolds in two-dimensional flows. Tracking LCS in flows is important for many applications such as planning energy optimal paths in the ocean and for predicting the evolution of various physical and biological processes in the ocean. The proposed strategy which tracks attracting LCS and unstable manifolds in real-time through direct computation of the local finite time Lyapunov exponent field, does not require global information about the dynamics of the surrounding flow, and is based on local sensing, prediction, and correction. The collaborative control strategy is implemented on a team of robots and theoretical guarantees for the tracking and formation keeping strategies are presented. We demonstrate the performance of the tracking strategy in simulation using actual ocean flow data and experimental flow data generated in a tank. The strategy is validated experimentally using a team of micro autonomous surface vehicles in an actual fluid environment.